# How do you identify the important parts of g(x)= x^2-4x+4 to graph it?

Oct 5, 2015

Intercept: 4
Minimum value: $\left(2 , 0\right)$

#### Explanation:

From the equation, any number behind $x$ is the intercept. So from this equation you know that the intercept is $4$.

Next, complete the square so that the equation is in the form of $a {\left(x + h\right)}^{2} + k$. This will give you the minimum points of the graph.

If you don't know how to complete a square, it's like this:

1. Divide the coefficient of $x$ by $2$
2. Take the square out of the $x$, so you will get ${\left(x - 2\right)}^{2}$
3. Then square the $2$ inside the bracket, which gets you ${\left(x - 2\right)}^{2} - 4 + 4$
4. Finally simplify the equation. ${\left(x - 2\right)}^{2}$

Since there is no number after the brackets, the minimum value of $y$ is $0$.

Minimum points= $\left(2 , 0\right)$
(Always switch the negative signs into positive and vice versa for the completed square!)

graph{x^2-4x+4 [-7.19, 8.614, -0.26, 7.64]}